Multiset Estimates and Combinatorial Synthesis

TL;DR

This paper introduces a novel ordinal assessment method using multiset estimates, explores their operations, and applies combinatorial synthesis to evaluate alternatives with numerical examples.

Contribution

It develops a new multiset-based assessment framework, including operations and integration with combinatorial synthesis, for ordinal evaluation of alternatives.

Findings

Defined basic assessment problems with multiset estimates

Presented operations like integration, comparison, and aggregation of multiset estimates

Illustrated methods with numerical examples

Abstract

The paper addresses an approach to ordinal assessment of alternatives based on assignment of elements into an ordinal scale. Basic versions of the assessment problems are formulated while taking into account the number of levels at a basic ordinal scale [1,2,...,l] and the number of assigned elements (e.g., 1,2,3). The obtained estimates are multisets (or bags) (cardinality of the multiset equals a constant). Scale-posets for the examined assessment problems are presented. 'Interval multiset estimates' are suggested. Further, operations over multiset estimates are examined: (a) integration of multiset estimates, (b) proximity for multiset estimates, (c) comparison of multiset estimates, (d) aggregation of multiset estimates, and (e) alignment of multiset estimates. Combinatorial synthesis based on morphological approach is examined including the modified version of the approach with multiset estimates of design alternatives. Knapsack-like problems with multiset estimates are briefly described as well. The assessment approach, multiset-estimates, and corresponding combinatorial problems are illustrated by numerical examples.